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Article On the Resolvent of the Laplace-Beltrami Operator in Hyperbolic Space(Cambridge Univ Press, 2015) Guseinov, Gusein Sh.In this paper, a detailed description of the resolvent of the Laplace-Beltrami operator in n-dimensional hyperbolic space is given. The resolvent is an integral operator with the kernel (Green's function) being a solution of a hypergeometric differential equation. Asymptotic analysis of the solution of this equation is carried out.Article Citation - WoS: 1Citation - Scopus: 1Prediction of the Onset of Shear Localization Based on Machine Learning(Cambridge Univ Press, 2023) Akar, Samet; Ayli, Ece; Ulucak, Oguzhan; Ugurer, DorukPredicting the onset of shear localization is among the most challenging problems in machining. This phenomenon affects the process outputs, such as machining forces, surface quality, and machined part tolerances. To predict this phenomenon, analytical, experimental, and numerical methods (especially finite element analysis) are widely used. However, the limitations of each method hinder their industrial applications, demanding a reliable and time-saving approach to predict shear localization onset. Additionally, since this phenomenon largely depends on the type and parameters of the constitutive material model, any change in these parameters requires a new set of simulations, which puts further restrictions on the application of finite element modeling. This study aims to overcome the computational efficiency of the finite element method to predict the onset of shear localization when machining Ti6Al4V using machine learning methods. The obtained results demonstrate that the FCM (fuzzy c-means) clustering ANFIS (adaptive network-based fuzzy inference system) has given better results in both training and testing when it is compared to the ANN (artificial neural network) architecture with an R-2 of 0.9981. Regarding this, the FCM-ANFIS is a good candidate to calculate the critical cutting speed. To the best of the authors' knowledge, this is the first study in the literature that uses a machine learning tool to predict shear localization.Article Citation - Scopus: 1Air Refueling Optimisation for More Agile and Efficient Military Deployment Operations(Cambridge Univ Press, 2022) Toydas, M.; Malyemez, C.Strategic airlift is a crucial capability for any country that wants to protect its global interests around the world. Air refueling may offer more agile and efficient airlift capabilities by increasing cargo aircraft payload and shortening airlift time. We investigated whether air refueling can shorten the total time of an airlift operation and decrease the number of cargo aircraft sorties required in a deployment scenario, especially where the distance between origin and destination is within the range of cargo aircraft. We introduced two mathematical models to compare the total airlift time and number of cargo aircraft required for given origin-destination and tanker base locations and total freight to be moved. We optimised initial cargo and fuel amount for cargo aircraft along with rendezvous point coordinates to minimise total airlift time. We used a numerical example to show that substantial airlift time and cargo aircraft sortie savings are possible through air refueling.Article Citation - WoS: 6Citation - Scopus: 7DISTRIBUTIONS OF RANDOM VARIABLES INVOLVED IN DISCRETE CENSORED δ-SHOCK MODELS(Cambridge Univ Press, 2023) Chadjiconstantinidis, Stathis; Eryilmaz, SerkanSuppose that a system is affected by a sequence of random shocks that occur over certain time periods. In this paper we study the discrete censored delta-shock model, delta <= 1 , for which the system fails whenever no shock occurs within a -length time period from the last shock, by supposing that the interarrival times between consecutive shocks are described by a first-order Markov chain (as well as under the binomial shock process, i.e., when the interarrival times between successive shocks have a geometric distribution). Using the Markov chain embedding technique introduced by Chadjiconstantinidis et al. (Adv. Appl. Prob. 32, 2000), we study the joint and marginal distributions of the system's lifetime, the number of shocks, and the number of periods in which no shocks occur, up to the failure of the system. The joint and marginal probability generating functions of these random variables are obtained, and several recursions and exact formulae are given for the evaluation of their probability mass functions and moments. It is shown that the system's lifetime follows a Markov geometric distribution of order (a geometric distribution of order under the binomial setup) and also that it follows a matrix-geometric distribution. Some reliability properties are also given under the binomial shock process, by showing that a shift of the system's lifetime random variable follows a compound geometric distribution. Finally, we introduce a new mixed discrete censored delta -shock model, for which the system fails when no shock occurs within a -length time period from the last shock, or the magnitude of the shock is larger than a given critical threshold . gamma > 0. Similarly, for this mixed model, we study the joint and marginal distributions of the system's lifetime, the number of shocks, and the number of periods in which no shocks occur, up to the failure of the system, under the binomial shock process.Article Citation - WoS: 14Citation - Scopus: 17Hybrid Nanocomposites of Elastomeric Polyurethane Containing Halloysite Nanotubes and Poss Nanoparticles: Tensile, Hardness, Damping and Abrasion Performance(Cambridge Univ Press, 2020) Mohamed, Salma Taher; Tirkes, Seha; Akar, Alinda Oyku; Tayfun, UmitThermoplastic polyurethane (TPU) matrix was reinforced with polyhedral oligomeric silsesquioxane (POSS) and halloysite nanotubes (HNT), both separately and combined. Composite samples were fabricated using a melt-compounding method. Characterization of the composites obtained was performed via tensile and hardness tests, melt-flow index measurements (MFI), abrasion tests, dynamic mechanical analysis (DMA) and scanning electron microscopy (SEM) to investigate the mechanical performance, flow behaviour, tribological characteristics, thermo-mechanical response and morphological properties. The greatest tensile strength value was obtained for the smallest HNT content. Further addition of HNT resulted in agglomerations for both POSS and HNT particles. The shore hardness of TPU was enhanced by filler inclusions. The TPU/POSS composites displayed significant improvement in terms of abrasion resistance compared to TPU at lower loading levels. The DMA study showed that composites containing 0.5% POSS and 1.0% HNT displayed the greatest storage modulus. The glass-transition temperature of TPU shifted to smaller values with the addition of both nanoparticles. The HNT inclusions increased the MFI value of TPU because of their large aspect ratio. Homogeneous mixing of nanoparticles in the TPU matrix was confirmed by a SEM study of the composites. Their dispersion decreased as the concentrations of POSS and HNT increased. An adjuvant effect of POSS with HNT was achieved in their hybrid composites.
